Subgroups — C₃×C₄₉×D₅₅ #30633464

Order 16170.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₁×C₄₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₄₉×D₅₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×D₁₁×C₄₉	—	5	1	no	maximal, Hall
4	C₅×C₁₁×C₄₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₇×D₅₅	C₇	1	1	yes	maximal, characteristic
6	C₃×C₁₁×C₄₉	D₅	1	1	yes	characteristic, complemented, Hall
7	C₃×D₅×C₄₉	—	11	1	no	maximal, Hall
8	C₃×C₅×C₇×C₁₁	C₂×C₇	1	1	yes	characteristic
9	D₁₁×C₄₉	—	5	1	no	Hall
10	C₇×D₅₅	C₃×C₇	1	1	yes	characteristic
11	C₃×C₅×C₄₉	D₁₁	1	1	yes	characteristic, complemented, Hall
12	C₁₁×C₄₉	C₃×D₅	1	1	yes	characteristic, complemented, Hall
13	D₅×C₄₉	—	11	1	no	Hall
14	C₃×C₇×D₁₁	—	5	1	no	—
15	C₅×C₇×C₁₁	C₂×C₃×C₇	1	1	yes	characteristic
16	C₃×D₅₅	C₄₉	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₃×C₄₉	—	55	1	no	Hall
18	C₅×C₄₉	C₃×D₁₁	1	1	yes	characteristic, complemented, Hall
19	C₃×C₇×C₁₁	C₇×D₅	1	1	yes	characteristic
20	C₃×C₇×D₅	—	11	1	no	—
21	C₃×C₅×C₁₁	C₂×C₄₉	1	1	yes	characteristic, complemented, Hall
22	C₇×D₁₁	—	5	1	no	—
23	C₃×C₄₉	D₅₅	1	1	yes	characteristic, direct product factor, Hall
24	D₅₅	C₃×C₄₉	1	1	yes	characteristic, direct product factor, Hall
25	C₃×C₅×C₇	C₇×D₁₁	1	1	yes	characteristic
26	C₂×C₄₉	—	55	1	no	Hall
27	C₇×C₁₁	C₃×C₇×D₅	1	1	yes	characteristic
28	C₇×D₅	—	11	1	no	—
29	C₃×D₁₁	—	5	1	no	Hall
30	C₅×C₁₁	C₂×C₃×C₄₉	1	1	yes	characteristic, complemented, Hall
31	C₄₉	C₃×D₅₅	1	1	yes	characteristic, direct product factor, Sylow
32	C₂×C₃×C₇	—	55	1	no	—
33	C₅×C₇	C₃×C₇×D₁₁	1	1	yes	characteristic
34	C₃×C₁₁	D₅×C₄₉	1	1	yes	characteristic, complemented, Hall
35	C₃×D₅	—	11	1	no	Hall
36	D₁₁	—	5	1	no	Hall
37	C₃×C₇	C₇×D₅₅	1	1	yes	characteristic
38	C₃×C₅	D₁₁×C₄₉	1	1	yes	characteristic, complemented, Hall
39	C₂×C₇	—	55	1	no	—
40	C₁₁	C₃×D₅×C₄₉	1	1	yes	characteristic, complemented, Sylow
41	D₅	—	11	1	no	Hall
42	C₇	C₃×C₇×D₅₅	1	1	yes	characteristic
43	C₂×C₃	—	55	1	no	Hall
44	C₅	C₃×D₁₁×C₄₉	1	1	yes	characteristic, complemented, Sylow
45	C₃	C₄₉×D₅₅	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	—	55	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₄₉	D₅₅
commutator, hypocenter	C₅×C₁₁	C₂×C₃×C₄₉
Frattini	C₇	C₃×C₇×D₅₅
Fitting	C₃×C₅×C₁₁×C₄₉	C₂
socle	C₃×C₅×C₇×C₁₁	C₂×C₇
prime radical	C₃×C₇×D₅₅	C₇
cosocle	C₅×C₇×C₁₁	C₂×C₃×C₇
LCS	G ▷ C₅×C₁₁
UCS	C₁ ◁ C₃×C₄₉

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃×C₅×C₁₁×C₄₉	C₂	semidirect
2. C₄₉×D₅₅	C₃	direct (N × H)
4. C₅×C₁₁×C₄₉	C₂×C₃	semidirect
6. C₃×C₁₁×C₄₉	D₅	semidirect
11. C₃×C₅×C₄₉	D₁₁	semidirect
12. C₁₁×C₄₉	C₃×D₅	semidirect
16. C₃×D₅₅	C₄₉	direct (N × H)
18. C₅×C₄₉	C₃×D₁₁	semidirect
21. C₃×C₅×C₁₁	C₂×C₄₉	semidirect
23. C₃×C₄₉	D₅₅	direct (N × H)
24. D₅₅	C₃×C₄₉	direct (N × H)
30. C₅×C₁₁	C₂×C₃×C₄₉	semidirect
31. C₄₉	C₃×D₅₅	direct (N × H)
34. C₃×C₁₁	D₅×C₄₉	semidirect
38. C₃×C₅	D₁₁×C₄₉	semidirect
40. C₁₁	C₃×D₅×C₄₉	semidirect
44. C₅	C₃×D₁₁×C₄₉	semidirect
45. C₃	C₄₉×D₅₅	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₅×C₁₁×C₄₉	2
C₄₉×D₅₅	3
C₃×D₁₁×C₄₉	5
C₃×C₇×D₅₅	7
C₃×D₅×C₄₉	11

Subgroups — C3×C49×D55 #30633464

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄₉×D₅₅ #30633464